Standard +0.3 This is a straightforward proof by induction with a summation involving exponentials. While it's a Further Maths topic (making it slightly above average), the structure is completely standard: verify base case n=1, assume for n=k, prove for n=k+1 by adding the next term and factoring out 3^k. The algebra is routine and requires no novel insight—just careful manipulation of geometric series terms.
Show sufficient working to justify correct expression
B1
Clear statements of Induction processes, but first 4 marks must all be earned
[5]
## Question 5:
| B1 | Verify result true when $n = 1$
| M1* | Add next term in series
| DepM1 | Attempt to obtain $3^{k+1}$ correctly
| A1 | Show sufficient working to justify correct expression
| B1 | Clear statements of Induction processes, but first 4 marks must all be earned
**[5]**
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